Ratio Testing for Changes in the Long Memory Indexes

Abstract

This paper considers the problem of detecting for breaks in the long memory indexes of Gaussian observations having long-range dependence. Under the null hypothesis,
the asymptotic distribution of the proposed ratio tests converges to a functional of fractional Brownian motion. Under the alternative hypothesis, the ratio tests diverge
to infinity as the sample size grows. These results show that the reject rate seriously depends on the magnitude of change points. Finally, the Monte Carlo study presents that our test has reasonably good size and power properties.